Problem: Evaluate the definite integral. $\int^{14}_{0}10e^x\,dx = $ Choose 1 answer: Choose 1 answer: (Choice A) A $140e^{14}$ (Choice B) B $\dfrac{5e^{14}}{7}-10$ (Choice C) C $10e^{14}-10$ (Choice D) D None of the above
Explanation: First, use the exponent rule: $\begin{aligned}\int^{14}_{0}10e^x\,dx =~10e^x\Bigg|^{14}_{{0}}\end{aligned}$ Second, plug in the limits of integration: $(10e^{{14}})-(10e^{{0}}) = 10(e^{14}-1)$. The answer: $\int^{14}_{0}10e^x\,dx~=~10(e^{14}-1)$